Signal Processing Stack Exchange
Signal Processing Stack Exchange

Questions tagged [interpolation]

Interpolation is a method of constructing new data points within the range of a discrete set of known data points.

Usually, it is required to interpolate (i.e. estimate) the value of that function for an intermediate value of the independent variable. This may be achieved by curve fitting or regression analysis.

Source: Wikipedia.

298 questions
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Calculating the PDF of a waveform from its samples

A while ago I was trying different ways to draw digital waveforms, and one of the things I tried was, instead of the standard silhouette of the amplitude envelope, to display it more like an oscilloscope. This is what a sine and square wave look…
endolith
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Frequency-domain zero padding - special treatment of X[N/2]

Suppose we wish to interpolate a periodic signal with an even number of samples (e.g. N=8) by zero-padding in the frequency domain. Let the DFT X=[A,B,C,D,E,F,G,H] Now let's pad it to 16 samples to give Y. Every textbook example and online tutorial…
finnw
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How can I design Nyquist interpolation filters with the Parks-McClellan algorithm?

We can easily design interpolation filters that obey certain frequency-domain constraints using the Parks-McClellan algorithm. However, it's not immediately clear how to enforce time-domain constraints; in particular, I'm interested in generating…
Oliver Charlesworth
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How to Resample Audio Using FFT or DFT

I'm down sampling voice audio by first performing an FFT, then only taking the parts of the result that I need, and then performing an inverse FFT. However, it's only working properly when I'm using frequencies that are both power of two, say…
thr
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Differences between filtering and polynomial regression smoothing?

What are the differences between classical low-pass filtering (with an IIR or FIR), and "smoothing" by localized Nth degree polynomial regression and/or interpolation (in the case of upsampling), specifically in the case where N is greater than 1…
hotpaw2
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How does subpixel image shifting using DFT really work?

I am trying to assess the quality of several image interpolation methods for an application that involves generating subpixel-shifted images. I thought I could compare the results of a subpixel shift using all these interpolation variants with some…
neuviemeporte
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Real-valued ringing when zero-padding odd-length FFT

So I'm trying to write a frequency-domain interpolator that zero-pads the frequency response of a signal and inverse transforms. There's two cases I have to deal with: Even-length response - have to split the $F_s/2$ bin because it's ambiguous. …
gct
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How can I automatically classify peaks of signals measured at different positions?

I have microphones measuring sound over time at many different positions in space. The sounds being recorded all originate from the same position in space but due to the different paths from the source point to each microphone; the signal will be…
Andy
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Whittaker-Shannon ($\mathrm{sinc}$) interpolation for a finite number of samples

Given an infinite number of samples $(N)$, a higher (or lower) number of samples $(cN)$ can be derived using sinc interpolation followed by sampling. How can this be applied to finite length signals? With $\mathrm{sinc}$ interpolation, one can…
Television
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Finding local peaks in-between samples

I have $n$ discrete samples of a seismic signal $y[n]$: I want to find local maxima in the signal. A naive test for if $y[n]$ is a maximum would be: $$y[n]: maxima \textbf{ if } y[n] > y[n-1] \textbf{ and } y[n] > y[n+1]$$ However the maxima are…
Andy
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What interpolation methods can I use to get the tightest fit for these curves?

I am working with MRI images of the brain that have certain areas marked by hand like and . I am trying to come up with an interpolating function that will let me describe such curves so that I can use machine learning techniques to automatically…
rdasxy
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When is cubic spline interpolation better than an interpolating polynomial?

The following plot is a slight variation of an example in a text book. The author used this example to illustrate that an interpolating polynomial over equally spaced samples has large oscillations near the ends of the interpolating interval. Of…
Ted Ersek
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Signal values we will 'miss' between sampling instances during sampling of band limited signals

According to the Nyquist–Shannon sampling theorem, any continuous time signal with a bandwidth $B$ smaller than Nyquist frequency $f_N=f_s/2$ (with $f_s$ the sampling frequency), which is sampled at sampling frequency $f_s$ can be perfectly…
Retinite
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Zero, First, Second ... nth-order Hold

The rectangular function is defined as: $$\mathrm{rect}(t) = \begin{cases} 0 & \mbox{if } |t| > \frac{1}{2} \\ \frac{1}{2} & \mbox{if } |t| = \frac{1}{2} \\ 1 & \mbox{if } |t| < \frac{1}{2}. \\ \end{cases}$$ The triangular function is defined…
Mark
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How do I use a Savitzky Golay filter to find local maxima (in between samples) in a discretely sampled 1D signal?

I have a seismic signal y(i): Here I have found one maximum: i=152.54, y=222.29 manually and plotted it in red. I want to find all maxima automatically. I read that the Savitzky Golay Filter (SGF) can be used to find smoothed estimates of both a…
Andy
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